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Standard – VIII(SIMO) - 2012
www.simoeducation.com © 2012 SIMO Education Page 1
SIMO EDUCATION
INDIAN MATHEMATICS OLYMPIAD (SIMO) 2012 SCREENING TEST
STANDARD VIII
Time : 90 mins Max. Marks : 120
Instructions:
The question paper contains 30 questions to be answered in 90 minutes
All questions have ONLY ONE correct answer.
Each question carries 4 marks. One mark would be deducted for every wrong answer. No
marks would be deducted for unattempted questions.
You can retain the Question paper with you after the Olympiad.
Fill the OMR sheet very carefully. Your name in the participation certificate will be the
same as the one you give here. Please leave space after initials.
01. A circle and square have same center and area. The radius of circle is 1. The area of octagon
formed by their intersection is given by 24 . Then α is equal to
(A) π+2 (B) 4- π (C) π-2 (D) 4+ π
02. Let r be any root of the equation x4-16x
3+62x
2-16x+1=0. Now consider the statements below.
I. |r|>1 II. |r|<10
Which of the above statements is/are always true?
(A)Only I (B) Only II (C) Both I and II (D) Neither I nor II
03. The largest prime factor of 72010
+72011
+72012
is
(A) 103 (B) 57 (C) 19 (D) None of these
04. Two triangles ABC and PQR are congruent. They are joined along an equal edge to form a new
triangle say XYZ. Also, angles of XYZ and ABC are same. If one of the sides of triangle PQR is 2
units, the possible are of triangle PQR is
(A) 2 sq units (B) 1 sq unit (C) Either A or B (D) Neither A nor B
05. The value of
2 3 42 3 42 3 4
2 3 4 is
(A) 10 (B) 75 (C) 92 (D) None
06. The sum of all digits of number given by 102012
-2012 is
(A) 18102 (B) 18106 (C) 18104 (D) None
07. If
1 12 2 6
13 3 7
xx
, then the value of x is
(A) ½ (B) ¼ (C) 3/8 (D) None
Standard – VIII(SIMO) - 2012
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08. x and y are integers such that -4<x,y<4. Also x(x-3)=y(y-3). Then number of possible values of
x+y is
(A) 7 (B) 8 (C) 9 (D) None
09. If (x2-3x+2) is a factor of (x
5-x
4-x
3+ax
2+bx+1) and x+2 is a factor of ax
2+bx+c, then c=
(A) 27 (B) -18 (C) Either A or B (D) Neither A nor B
10. Unit’s digit of (32012
+42012
+52012
) (72012
+82012
+92012
) is
(A) 2 (B) 4 (C) 6 (D) 8
11. x and y are integers such that 4x+3y2=2012. If x is even, then remainder obtained when x is
divided by 24 is
(A) 10 (B) 4 (C) Either A or B (D) Neither A nor B
12. Consider the following statements
I. product of two rational numbers is always rational
II. difference of two irrational numbers is always irrational
Which of the above statements is/are always true?
(A)Only I (B) Only II (C) Both I and II (D) Neither I nor II
13. ABCD is a rectangle such that AB=5cms and BC=12cms. The length of foot of perpendicular
from B onto AC is
(A) 30/13 (B) 40/13 (C) 60/13 (D) None of these
14. x and y are two natural numbers. Consider the following statements
I. x is odd II. y is odd III. x+y is odd IV x2 is even V. GCD(x,y)=1
It is known that ONLY ONE Of the above statements is correct. Identify it.
(A) III (B) V (C) IV (D) II
15. ABCD is a rectangular sheet of paper such that BC=180mm and AB=300mm. P is a point on
AD. The paper is folded along the line CP and it is observed that P falls on the line AB when folded.
The distance AP is equal to
(A) 100mm (B) 125mm (C) 150mm (D) 200mm
16. Sum of two primes is 36. Then their product is
(A) 203 (B) 299 (C) 323 (D) any of the above
17. ABCD is a square. P,Q are points on lines BC and DC such that areas of polygons ABP, APCQ
and ACD are equal. Then the ratio of area of triangle APQ to that of the square is
(A) 7:18 (B) 5:18 (C) 3:8 (D) 9:19
18. x,y,z,t,w are five positive numbers such that yt<zt<xy<yz<xw. Then the smallest of them is
(A) y (B) x (C) t (D) w
19. A, B, C, D and E are five points on plane such that E is at a distance of 2,3,5 and 6 units from
A,B,C and D respectively. Maximum possible area of the quadrilateral ABCD is
(A) 31.5 (B) 36.5 (C) 33.5 (D) None
Standard – VIII(SIMO) - 2012
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20. Priyanka is now three times as old as she was three years before she was as old as she is now.
Her age is now
(A) 12 (B) 15 (C) 16 (D) 18
21. Regular polygons P1, P2, P3 of equal sides are placed along edges of equilateral triangle ABC.
Side of triangle is equal to that of polygons. It is observed that the space around the triangle is
completely filled by these polygons. Now P1, P2, P3 and ABC form a bigger polygon say Q. Number
of sides of Q is
(A) 36 (B) 30 (C) 32 (D) None of these
22. A cycle chain with two links is shown below.
Similarly, the length of chain with 5 links is 27cms. Then, length of chain with 10 links is
(A) 54cms (B) 50cms (C) 52cms (D) None
23. l1 and l2 are parallel lines such that AB is a transversal with A on l1 and B on l2. C is a point on l1
such that AB=AC. Also D is a point on l2 such that BC=BD. If C and D are on same side of AB and
CDB =50o, acute angle made by transversal AB with l1 is
(A) 80o (B) 60
o (C) 20
o (D) None
24. If 21/2
.41/4
.81/8
.16x=1, then value of x is
(A) -11/32 (B) -1/4 (C) -13/24 (D) None
25. If (2x+y)(3x2+E)=(6x
3+7x
2y+4xy
2+4x
2+2xy+2x+y where E(x,y) is an expression in x and y, then
value of E when x=-2 and y=0 is
(A) 7 (B) 9 (C) 11 (D) None
Instructions for Questions 26 to 30
Each of these questions has a question and two statements I and II following it. Mark your option as
below. If you can answer the questions using,
statement I alone, mark A
statement II alone, mark B
ONLY on using both statements I and II, mark C
Cannot answer even after using both of them, mark D
26. a,b,c are integers. Is a=b=c?
I. a3+b
3+c
3=3abc II. 3a+4b+5c=24
27. Is ABCD rectangle?
I. Diagonals bisect each other II. Diagonals are equal
28. Is (x-1) a factor of abx3+(2a-b)x
2-(ab+2)x+b?
I. b=3 II. a=1
Standard – VIII(SIMO) - 2012
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29. Is x even natural number?
I. x2+y
2+1=2x II y=x
30. Is hexagon ABCDEF regular?
I. All sides of hexagon are equal II. All angles of hexagon are equal.
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